Part 4/7:
To visualize this concept, consider sketching an arbitrary curve between the values ( a ) and ( b ). In this case, the absolute maximum within this span could be identified at a peak, and the absolute minimum at the lowest dive in the curve over this interval.
Critical Points
Critical points play an important role in finding extrema—they are defined as values of ( x ) where the derivative ( f'(x) ) equals zero or does not exist. Identifying these points is crucial because they often indicate potential maximum or minimum values.